A priori error analysis for a mixed VEM discretization of the spectral problem for the Laplacian operator

Abstract

The aim of the present work is to derive error estimates for the Laplace eigenvalue problem in mixed form, implementing a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is spurious free and convergent. Optimal order of convergence for the eigenvalues and eigenfunctions are derived. Finally, we report numerical tests to confirm the theoretical results together with a rigorous computational analysis of the effects of the stabilization parameter, inherent for the virtual element methods, in the computation of the spectrum.